The Race

[soroban]

This is an oldie.


A, B and C have a 100-yard race.
A beats B by 10 yards.
B beats C by 10 yards.
By how much does A beat C?
Explain your answer.


Before some smarta\$\$ asks:
. . Yes, they start from the same place.
. . Yes, they start at the same time.
. . Yes, they run in the same direction.
.

 

[JumboJam]

If we assume all the racers run at a constant speed, then A beats C by 19 yards.

This can be done by finding the relative speeds of each racer.

• A finishes 100 yards at at some time t.
• B, who is 10 yards behind A, thus has a speed of 90/t.
• B thus finishes the race at time = 10t/9.
• C, who is 10 yards behind B, has a speed of 90/(10t/9) = 81 yards/ t seconds.
• Thus, at time t, C travels 81 yards.
• A is 19 yards ahead of C.

 

[Deleted member 4993]

This is an oldie.


A, B and C have a 100-yard race.
A beats B by 10 yards.
B beats C by 10 yards.
By how much does A beat C?
Explain your answer.


Before some smarta\$\$ asks:
. . Yes, they start from the same place.
. . Yes, they start at the same time.
. . Yes, they run in the same direction.
.

One more anti-smarta$$ assumption (beside constant speed) - they were running a straight sprint (i.e. constant velocity).

Oh by the way, they could not start from the same place at the same time (there is a law in Physics....) - just to be smart....